I've been researching cyclotomic FFTs.  There is a lot of literature (Fedorenko, Trifinov, Costa, etc.) about using this technique for calculating the syndrome and doing the Chien Search in Reed-Solomon decoders.  I'd like to know if anybody has actually used this in hardware.  The literature makes bold claims about the massive 100x efficiency gains, but it seems like it's only useful in software.  As far as I can tell, the advantage in hardware for a highly-parallel decoder (e.g., 64 symbols per cycle) over the conventional Horner Method is nonexistent.